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A251637 Square array read by antidiagonals containing in row n the multiples of prime(n) in A098550 in order of appearance. 6
2, 3, 4, 15, 9, 8, 14, 5, 15, 14, 22, 35, 25, 6, 6, 39, 11, 7, 35, 12, 12, 51, 13, 33, 21, 10, 21, 16, 38, 17, 26, 55, 28, 20, 27, 10, 69, 19, 85, 65, 44, 91, 45, 39, 20, 87, 23, 95, 34, 91, 99, 49, 85, 33, 22, 62, 29, 115, 57, 68, 52, 77, 63, 55, 45, 26, 74 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

T(n,k) = A251715(n,k)*A000040(n); A251715(n,k) = T(n,k)/A000040(n);

T(n,k) = A098550(A251716(n,k)); A251716(n,k) = A098551(T(n,k));

T(n,1) = A251618(n); for n > 4: T(n,2) = A000040(n);

conjecture: A098550 is a permutation of the positive integers iff A001221(n) = number of rows containing n.

A251541 = first column, and A251544 = third column for row numbers > 4. - Reinhard Zumkeller, Dec 16 2014

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

EXAMPLE

.   n   p |  first 14 multiples of p = prime(n) in A098550, n = 1..25

.  -------+-------------------------------------------------------------

.   1   2 |   2  4   8  14   6  12  16  10   20  22   26   28   32   18

.   2   3 |   3  9  15   6  12  21  27  39   33  45   51   18   24   36

.   3   5 |  15  5  25  35  10  20  45  85   55  65   30   95   40   50

.   4   7 |  14 35   7  21  28  91  49  63   42  56   77  119  133  161

.   5  11 |  22 11  33  55  44  99  77  66   88 165  143  121  187  110

.   6  13 |  39 13  26  65  91  52 117  78  104 195  143  130  156  221

.   7  17 |  51 17  85  34  68 119 153 102  187 136  170  255  221  204

.   8  19 |  38 19  95  57 133  76 171 114  152 209  247  190  285  228

.   9  23 |  69 23 115  46 161  92 138 207  184 253  299  345  230  276

.  10  29 |  87 29  58 145 203 116 174 261  232 319  377  290  435  348

.  11  31 |  62 31  93 155 124 217 279 186  341 403  248  465  310  372

.  12  37 |  74 37 111 185 148 259 222 333  296 407  555  370  629  481

.  13  41 | 123 41  82 205 164 287 246 369  451 328  410  533  615  492

.  14  43 |  86 43 129 215 172 301 387 258  473 344  430  645  559  516

.  15  47 |  94 47 329 141 235 188 282 423  517 376  470  611  705  564

.  16  53 | 106 53 265 159 212 371 318 477  424 583  689  530  795  636

.  17  59 | 118 59 177 295 236 413 354 531  649 472  767  590  885 1003

.  18  61 | 122 61 427 183 305 244 366 549  671 488  793  610  915  732

.  19  67 | 201 67 335 134 268 469 603 402  536 737  871  670 1005  804

.  20  71 | 142 71 213 355 284 497 426 639  568 781  710 1065  923  852

.  21  73 | 146 73 365 219 292 511 438 657  584 803  730  949 1095  876

.  22  79 | 158 79 237 395 316 553 474 711  632 869 1027  790 1185  948

.  23  83 | 249 83 581 166 415 332 498 747  913 664 1079  830 1245  996

.  24  89 | 178 89 267 445 356 623 534 801  712 979 1157  890 1335 1068

.  25  97 | 291 97 679 194 485 388 582 873 1067 776  970 1261 1455 1164 .

.  ---------------------------------------------------------------------

See also A251715 for a table with T(n,k)/p and A251716 for a table of indices of T(n,k) within A098550.

MATHEMATICA

rows = 25; (* f = A098550 *) Clear[f, row]; f[n_ /; n <= 3] := n; f[n_] := f[n] = Module[{k}, For[k=4, GCD[f[n-2], k] == 1 || GCD[f[n-1], k]>1 || MemberQ[Array[f, n-1], k], k++]; k]; row[n_] := row[n] = Module[{k, cnt}, Reap[For[k=1; cnt=0, cnt <= rows-n, k++, If[Divisible[f[k], Prime[n]], cnt++; Sow[f[k]]]]][[2, 1]]]; A251637 = Table[row[n-k+1][[k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Dec 17 2014 *)

PROG

(Haskell) when seen as table read by rows:

a251637 n k = a251637_tabl !! (n-1) !! (k-1)

a251637_row n= a251637_tabl !! (n-1)

a251637_tabl = adias $ map

   (\k -> filter

     ((== 0) . flip mod (fromInteger $ a000040 k)) a098550_list) [1..]

CROSSREFS

Cf. A098550, A000040, A251618 (first column), A001221, A251715, A251716.

Cf. A251541, A251544.

Sequence in context: A085100 A204983 A249623 * A035047 A037323 A065812

Adjacent sequences:  A251634 A251635 A251636 * A251638 A251639 A251640

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Dec 07 2014

STATUS

approved

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Last modified April 18 10:38 EDT 2019. Contains 322209 sequences. (Running on oeis4.)